Moisture adsorption by porous terahertz optical materials: a case study of artificial SiO<sub>2</sub> opals

V. E. Ulitko; V. E. Ulitko; G. R. Musina; V. M. Masalov; A. A. Gavdush; G. A. Emelchenko; V. V. Bukin; V. N. Kurlov; V. N. Kurlov; M. Skorobogatiy; G. M. Katyba; G. M. Katyba; G. M. Katyba; K. I. Zaytsev; K. I. Zaytsev; K. I. Zaytsev

doi:10.1364/OME.485646

1. Introduction

Different modalities of THz spectroscopy and imaging [1] offer a variety of applications in such demanding branches of science and technology, as medical diagnosis [2–4] and therapy [5], non-destructive testing of materials [6], industrial quality control [7], new-generation of wired [8–10] and wireless [11,12] communications, etc. All these rely on such features of THz waves, as their non-ionizing nature [5], quite small absorption by an ambient atmosphere (at sub-THz frequencies) [13], high penetration depth into a variety of bulk dielectrics, composites, and ceramics [14], sensitivity to the chemical composition and structural features of an analyte [15], and a reasonable resolution of the common THz optics, as compared to the lower-frequency waves [16].

Despite the interest in THz technology, different problems still restrain development of the THz opto-electronic devices and systems for real-life applications [1,2,16]. Among them, we particularly stress a poor variety of the THz optical material platforms (as compared to the visible and infrared ranges) and related fabrication difficulties [17,18]. Nowadays, a limited list of polymers and crystalline materials, with their low-to-moderate THz-wave absorption and discrete diversity of refractive indices, can be applied for the synthesis and optimization of either open-space or waveguide THz optics.

This problem can be mitigated, to some extent, using different artificial composites, as well as micro- or nano-porous THz optical materials, with tunable (mostly, pre-determined during synthesis) optical properties [17]. Consider a few examples:

• The first group is formed by the polymer-ceramic [19] and polymer-polymer [20] composites, mixtures of polymer with high-refractive-index [21,22] or magnetic [23] crystalline particles, polymer with embedded or sprayed low-dimensional materials, such as the carbon [24–26] and non-carbon [27] nanotubes, graphene [28] or MXenes flakes, [29]. Such composites yield advanced tunability of the THz optical properties via changes in their composition. However, they suffer from additional THz power loss and beam quality reduction due to the light scattering on the material heterogeneities.
• The second is represented by the porous materials with sub-wavelength dimensions of pores. THz optical properties of such media are managed via changes in the material porosity during synthesis. For example, one can consider microstructured polymers [30], porous aerogels [31], silk foam [32] porous ceramics [33], pressed high-refractive index micropowders [21], and 3D printed porous polymer elements [34]. Most recently, in Ref. [35,36], artificial opals based on nanoporous SiO$_2$ globules [37,38] were considered as a THz optical material, with a low-to-moderate THz-wave absorption and a wide refractive index tunability (thanks to changes in the material porosity by annealing). It allows obtaining complex-shaped THz optical surfaces by direct sedimentation of colloidal nanoparticles into a mold followed by annealing, thus, eliminating their labor-intensive mechanical processing. Despite the wide tunability and technological advantages, such materials also suffer from the additional THz-beam power loss.
• The third includes metamaterials and metasurfaces based on the complex-shaped sub-wavelength (or mesoscale) conductive (or dielectric) structures, such as wire metamaterials (media) [39,40] and metal hole arrays [41]. The THz response of such materials can be designed by changing the shape, orientation, alignment (order), and local electrodynamic properties of individual elements, either at the fabrication stage or during the exploitation. These materials still possess limited energy efficiency and low technological reliability, which makes them a subject of laboratory research.

All these materials are designed for operation in an ambient humid atmosphere. Therefore, they can interact with water vapour and adsorb water molecules, with the resultant undesirable and unpredictable changes in their THz dielectric response [42–44]. Due to the very high polarity of H$_2$O molecules, an impact of thus captured water (either in free or bond states) on the THz optical material performance can be crucial [15], which can even make impossible THz applications of such optics. Nevertheless, the effects of moisture adsorption by such porous THz optical materials, and related changes in their THz response have not been evaluated so far.

To address this issue, in this paper, THz pulsed spectroscopy is applied to study the moisture adsorption by artificial opals [35,36], that are assembled of the nanoporous SiO$_2$ particles by sedimentation of colloidal suspension and annealed at different temperatures in the $200$–$800^\circ$C range to manage their porosity and optical properties. Opals of two kinds are analyzed: both are made of $300$-nm-diameter particles, but possess distinct intraglobular structure and porosity. These opals are dehydrated in vacuum and then exposed to a humid atmosphere with $82.0 \pm 2.0\%$ relative humidity. Meanwhile, the evolution of their THz complex dielectric permittivity is studied in situ in the $0.5$–$2.5$ THz range. The observed changes in the THz dielectric response are analyzed using the sum rule and adsorption process models. We demonstrate strong changes in the effective THz dielectric response of the optical material, that depend on both the nanoparticles type and annealing conditions. This effect is general to all porous THz optics and, thus, should be taken into account during synthesis and implementation of such materials in THz applications.

2. Materials and methods

2.1 Sample preparation

Preliminary purified (by rectification) tetraethoxysilane (TEOS, $98$%), cyclohexane (CH, $99.9$%), ammonium hydroxide (NH$_4$(OH), $99,9$%) and L-arginine ($99$%), as well as deionized water ($18$ M$\Omega \cdot \mathrm {cm}$) were used to synthesize spherical $300$-nm-diameter SiO$_2$ nanoparticles. At first the SiO$_2$ seeds with a diameter of $\sim 30$ nm were synthesized by the heterogeneous hydrolysis of TEOS in an aqueous solution in the presence of L-arginine ($7.5$ mM) as a catalyst [45,46] for better SiO$_2$-particle monodispersity. Later, the two different techniques to grow these seeds were used for submicron SiO$_2$ nanoparticles obtaining, with their distinct internal structure, density, and porosity (Fig. 1):

• The Shell-like particles were obtained by the regrowth of SiO$_2$ seeds in an alcohol–water–ammonia mixture using the modified Stober–Fink–Bohn method [38,45]. This multistage growth process resulted in the $300$-nm-diameter spherical Shell-like SiO$_2$ particles with the porosity of $20-23\%$ (by volume), a smoothed surface, a multilayer internal structure, and $<3\%$ deviations in the diameter (Figs. 1(a), (b)) [47].
• The Berry-like ones were obtained by the regrowth of SiO$_2$ seeds using the heterogeneous hydrolysis of TEOS in an aqueous solution in the presence of L-arginine ($\sim 2$ mM) [46]. The particles were grown under constant stirring of the solution (Elmi TW-$2.02$ magnetic stirrer) at the $55$–$65^{\circ}$C temperatures (a water thermostat). The resultant Berry-like particles have the porosity of $10\%$ and a rough surface (Figs. 1(c), (d)). The deviation of the particle diameter from the average value was no more than $2\%$.

Fig. 1. Spherical $300$-nm-diameter SiO$_2$ nanoparticles grown by the two different techniques. (a),(b) A schematic and a scanning electron microscopy image, correspondingly, for the Shell-like particles. (c),(d) Equal data for the Berry-like particle. Images presented in panels (b) and (d) are reprinted from the ope-access Ref. [35] with the permission from the Optica Publishing Group.

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Thus fabricated SiO$_2$ nanoparticles of two kinds were then sedimented from a colloidal suspension onto a flat substrate to obtain bulk opal matrices – i.e., globular crystals with the face-centered cubic lattice [35]. These matrices were dried and annealed at temperatures of $200$, $400$, $600$, and $800^\circ$C for $24$ hours, in order to achieve different internal structure and porosity of the resultant samples; see Ref. [35]. After the annealing, the samples were cut into pieces, grinded and polished to achieve flats with the thickness of $\simeq 1$ mm, the surface area of $>1$ cm$^2$, and the small surface roughness at the THz-wavelength scale ($\ll \lambda$).

It is worth noting that vacuum dehydration was used rather than the low-temperature annealing as an absorbent regeneration technique. For this, the flats were stored for a few days in a vacuum desiccator (SB-2, Sanplatec, Japan) before their THz pulsed spectroscopy.

2.2 THz pulsed spectrometer and dielectric properties reconstruction

The samples were characterized using the in-house transmission-mode THz pulsed spectrometer, shown in Fig. 2(a) and detailed in Refs. [48,49]. It uses a pair of photoconductive antennas to emit and detect THz pulses [50] and a vacuumized ($\sim 10^{-3}$ mbar) THz beam path to prevent an impact of water vapour in an ambient laboratory atmosphere on the measured data. This system features the spectral operation range of $0.5$–$2.5$ THz and the spectral resolution as high as $\simeq 0.015$ THz.

Fig. 2. THz pulsed spectrometer with a vacuumized beam path and a sample chamber designed to study the moisture adsorption. (a) Photo of the THz pulsed spectrometer with the THz beam highlighted in blue; OAPM and PCA stand for an off-axis parabolic mirror and a photoconductive antenna. (b) Schematic of the sample chamber, with a sample is being handled either in vacuum or a humid atmosphere; the central rod allows to switch between the reference and sample apertures.

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To study interactions between water vapor and a sample, the latter was handled in a sample chamber (Fig. 2(b)), that is mounted in the THz beam path and connected to the separate humidity chamber. For simplicity, the humidity chamber is not considered here, since it was detailed in Ref. [43]. In the humidity chamber, a stabilized atmosphere was prepared, with the temperature of $\simeq 25^{\circ}$C and the relative humidity of $82.0 \pm 2.0\%$, as measured in situ by the thermohygrometer (Testo $635$, Germany), with an accuracy of $\pm ~0.1^\circ$C and $\pm ~0.1\%$, correspondingly. The sample chamber is separated from the humid one (by a valve) and from the THz beam path (by $20$-$\mu$m-thick mylar films, transparent at THz frequencies and thin enough to avoid standing waves). At the beginning of the experiment, the sample chamber was vacuumized ($\sim 10^{-3}$ mbar), and, thus, a sample was in a dehydrated state; for this, the valve between the humid and sample chambers was closed. Then, a sample was exposed to the humid atmosphere; for which the valve was opened, and the humid atmosphere filled up the sample chamber. The volume of the humidity chamber is much larger than that of the sample one; thus, the resultant atmosphere in both chambers is equal to the initial in the humidity chamber.

Each sample was measured by the THz pulsed spectrometer both in dehydrated state and during the moisture adsorption with the time step of $4$ min, until this process saturated. In Fig. 3, THz waveformes $E_{\mathrm {s}}(t)$ and their Fourier spectra $\widetilde {E}_{\mathrm {s}}(\nu )$, that correspond to the THz-wave transmission through the opals of two kinds in the dehydrated (dried) and hydrated (moisturised) states. Furthermore, photos of opals before and after exposure to a humid atmosphere are shown for both the Shell-like and Berry-like opals.

Fig. 3. THz pulsed spectroscopy of opals in a humid atmosphere. (a)–(c) THz waveforms $E \left ( t \right )$ and their Fourier spectra $E \left ( \nu \right )$ that correspond to the THz-wave transmission through the dehydrated (dried) and hydrated (moisturized, $2$-hours-long exposure to a humid atmosphere) opals based on the Shall-like particles. The reference THz signals correspond to the THz beam passed through an empty aperture, without a sample. (d) Photo of the dried and moisturised opals based on the Shall-like particles. (e)-(h) Equal data for opals based on the Berry-like particles.

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For each step, two THz waveforms were detected in the identical conditions: a sample one passed through the apertures with a sample atop; and a reference one passed through an equal opened aperture. As shown in Fig. 2(b), position between the sample and reference apertures was switched in situ using a sliding panel. It takes $\sim 10$ sec to collect a single THz waveform and to switch between the sample and reference apertures, which is much shorter than the $\sim 2$-hour-long adsorption process. Thus, the sample hydration was assumed to be constant during a single measurement.

We did not observe any notable changes in geometry and thickness of opals due to the water adsorption. Measurements by micrometer revealed that the thickness of all sample before and after the adsorption was constant. Since the dimensions of SiO$_2$ globules ($300$ nm) and the domains of colloidal crystal formed by these globules ($\sim 1$ $\mu$m) are negligibly small at the scale posed by the THz wavelengths, we assumed our sample to be homogeneous, and characterized their effective THz dielectric response at THz frequencies. Furthermore, due to such a small diameter of colloidal nanoparticles, we do not expect any notable variations in the water adsorption properties over the sample surface.

Using thus collected sample and reference THz waveforms, we retrieved the frequency-dependent THz complex dielectric permittivity $\widetilde {\varepsilon }$ and dynamic conductivity $\sigma$ [51]:

(1)$$\widetilde{\varepsilon} = \varepsilon' - i \varepsilon^{\prime\prime}, \qquad \sigma = \omega \varepsilon_\mathrm{0} \varepsilon^{\prime\prime},$$

for each opal sample in dehydrated state, as well as at different steps of the adsorption process. Here, $\varepsilon '$ and $\varepsilon ''$ are real and imaginary dielectric permittivity, respectively, $\omega = 2 \pi \nu$ is an angular frequency and $\varepsilon _\mathrm {0} = 8.854 \times 10^{-12}$ F m$^{-1}$ is the vacuum permittivity. The functions $\widetilde {\varepsilon }$ is estimated via minimization of the following vector error functional [52]:

(2)$$\widetilde{\varepsilon} = \mathrm{argmin}_{\widetilde{\varepsilon}} \left[ \Phi \right], \qquad \Phi=\left(\begin{array}{c} |H_{\mathrm{exp}}|-|H_{\mathrm{theory}}(\nu)|\\ \phi[H_{\mathrm{exp}}]-\phi[H_{\mathrm{theory}}(\nu)] \end{array}\right).$$

Here, $H_{\mathrm {exp}}$ is the experimental transfer function, which is calculated as a ratio of the measured sample and reference spectra

(3)$$|H_{\mathrm{exp}}|=\frac{\widetilde{E}_{\mathrm{s}}(\nu)}{\widetilde{E}_{\mathrm{r}}(\nu)}=\frac{\mathfrak{F}[E_{\mathrm{s}}(t)]}{\mathfrak{F}[E_{\mathrm{r}}(t)]},$$

where $\mathfrak {F}[\dots ]$ is a direct Fourier transform, $|\dots |$ and $\phi [\dots ]$ are the modulus and phase operators, respectively. $H_{\mathrm {theory}}$ is the theoretical transfer function for the plane-parallel plate (flat / window), that relied on the Fabry-Perot model for the finite number of resonances (satellites) and that is based on the Fresnel formulas and the Bouger-Lambert-Beer law [51–53]. Finally, we notice that the sample thickness was accounted during the THz dielectric permittivity reconstruction; the thickness was, first, measured by micrometer and, then, clarified numerically during the THz signal processing as detailed in Ref. [51]. For the detailed description of the THz data processing see Refs. [43,51], or another research works by our group. In this way, at different steps of the adsorption process, THz dielectric response was estimated for opals based on the Shell- and Berry-like particles and annealed at the temperatures of $200$–$800^\circ$C.

In Figs. 4(a)–(c), we show evolution of the $\varepsilon '$, $\varepsilon ''$, and $\sigma$-curves, respectively, during adsorption for a representative opal based on the Shell-like nanoparticles and annealed at $200^\circ$C; while in panels (d)–(f), similar data are shown for those based on the Berry-like. For both samples, pronounces changes in the THz dielectric curves during the water uptake are evident, while for the Shell-like, these changes are considerably larger. Adsorption of water leads to the increase in both real $\varepsilon '$ and imaginary $\varepsilon ''$ dielectric permittivity within the analyzed frequency range, while the resultant dielectric response still has no resonant spectral features. Such a behavior of the THz spectra can be attributed to a high dipole moment of H$_2$O molecules, as well as to the relaxation-like THz response of liquid water (free, bond, and confined) [15,35,42]. Quite similar evolution of the THz response was observed for all samples, with some differences in the amount of adsorbed water (as evident from the magnitude of the observed dielectric permittivity changes) and the adsorption kinetics (as follows from the different adsorption saturation times).

Fig. 4. THz pulsed spectroscopy of opals during the moisture adsorption. (a)–(c) Real $\varepsilon '$ and imaginary $\varepsilon ''$ dielectric permittivity, and dynamic conductivity $\sigma$ of a representative opal based on the Shell-like particles and annealed at $200^\circ$C. (d)–(f) Equal data for opal based on the Berry-like particles. Duration of a sample exposure to a humid atmosphere ($82.0 \pm 2.0\%$) is coded by the color bars.

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2.3 Estimation of the adsorption parameters

An amount of the absorbed water was retrieved roughly based on the THz data using the sum rule [54]

(4)$$\int_0^\infty \sigma d \nu = \frac{ \pi q^2}{ 2 m } N,$$

that defines a relationship between the number of charges (dipoles) $N$ underlying the dielectric response of an analyte, and the integral (over the positive frequencies) dynamic conductivity, where $q$ and $m$ stand for the effective charge and mass of a single carrier. Since no information about $q$ and $m$ is available, only qualitative values of $N$ can be estimated and compared for the analyzed opals at different stages of adsorption.

Considering that the dynamic conductivity spectrum $\sigma$ is formed additively by different electro-dipole excitations of matter (such as the non-local response of a free carriers, local resonance, and mostly local relaxation-like responses of polar molecular bounds in the THz range), which is a common assumption in optical spectroscopy [15,44]. Then, taking into account only the additive part of conductivity associated with the water uptake, the number of adsorbed H$_2$O molecules is given by [43]

(5)$$N \propto \int_{\nu_\mathrm{min}}^{\nu_\mathrm{max}} (\sigma_\mathrm{moist}-\sigma_\mathrm{dried}) d \nu.$$

where $\sigma _\mathrm {dried}$ and $\sigma _\mathrm {moist}$ stand for the conductivity of dehydrated and moisturized samples. This approach is quite approximate. First, it is due to the unknown $q$ and $m$ in Eq. (4). Second it is due to the finite range of dynamic conductivity integration in Eq. (5) (namely, from $\nu _\mathrm {min} = 0.5$ THz to $\nu _\mathrm {max} = 2.5$ THz, as defined by the THz pulsed system sensitivity), while water contributes to the THz response of an analyte in a much broader range [15]. Third, hydration of polar molecules and related changes in the THz dielectric response of water in hydration shells (as compared to free water) can also play an important role in formation of the THz response of an analyte [15]. Nevertheless, Accounting for the hydration effects is quite a daunting task, while the simplified approached, that is given by Eq. (5), and that involves linear decomposition of the conductivity spectrum, provides quite reasonable predictions, as evident from Refs. [42–44].

Such qualitative knowledge about water content in a sample makes possible analysis of the adsorption kinetics using the well-known models of the adsorption mass transfer mechanisms [55–57]. A standard pseudo first order model (PFOM) is usually applied to describe the so-called Landmuir adsorption with a purely exponential character [57]

(6)$$N \propto 1 - e^{- \alpha t}$$

and the pseudo first order rate constant $\alpha$ in [hours$^{-1}$] as a parameter. In Refs. [42,43], this model was used to interpret the THz data.

When the adsorption kinetics is more complex, such as that observed below for the SiO$_2$ opal samples, it is convenient to resort to another model with more parameters. Among them, we considered the stretched exponential model (SEM) [57]

(7)$$N \propto 1 - e^{\left( - \left(\alpha_\mathrm{SEM} t \right)^{\beta_\mathrm{SEM}}\right)}$$

which is semi-empirical, also has the adsorption rate constant $\alpha _\mathrm {SEM}$ in [hours$^{-1}$] as a parameter and accounts for the non-exponential character of a transient process via the parameter $\beta _\mathrm {SEM}$.

3. Results

In Figs. 5(a) and (b), a time-dependent number of the adsorbed water molecules $N$ is shown for opals based on both the Shell- and Berry-like globules, correspondingly, where the experimental data (markers) is approximated by SEM (dashed curves; Eq. (7)). For comparison, the experimental data approximation by the PFOM is also shown (dotted curves; Eq. (6)), from which we notice a disagreement between this model and our experimental data, that justifies the non-exponential character of a transient process. In Fig. 5(c), equilibrium (at $t = 2$ hours) experimental $N$ values are depicted, that correspond to the transient process saturation.

Fig. 5. Kinetics of the water vapour adsorption by opals annealed at $200$–$800^\circ$C. (a),(b) Evolution of the number of adsorbed water molecules $N$ during exposure of opals, made of the Shell- and Berry-like particles, respectively, to a humid atmosphere ($82.0 \pm 2.0\%$), where the experimental data (markers) are fitted by SEM and PFOM (curves). (c) Equilibrium values of $N$, corresponding to the saturated transient process (at $2$ hours). (d) Parameters of SEM for the kinetics of moisture adsorption by the Shell- and Berry-like opals, respectively.

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From Fig. 5, we notice that, for opals annealed at $200$, $400$, and $800^\circ$C, the adsorption process saturates during the $2$-hour-long exposure, while for opals at $600^\circ$C, the transient process is almost saturated (it is assumed to be saturated at $2$-hours in Fig. 5(c)). Opals based on Shell-like particles adsorb more water at all annealing temperatures, which is attributed to the higher porosity of such materials [35,58]. At the lower annealing temperatures of $200$–$600^\circ$C, this difference between two types of opals is more pronounced, while it is minimal at $800^\circ$. For both types of opals, $N$ decreases with annealing temperature (except for the opals based on the Berry-like particles annealed at $200^\circ$C and $400^\circ$C; see the Discussions section), which correlates with a decrease in the material porosity (or the effective area of the highly-evaluated surface formed by pores), and a decrease in the number of the active sites in the analyte [35,58]. It correlates with the earlier results of a water vapour adsorption analysis by opal structures [59] and with a thermal gravimetric analysis from Ref. [60], where annealing at high temperatures ($> 700^\circ$C) caused the least water absorption by opals.

Figure 5(a)-(b) shows that SEM (Eq. (7)) yield accurate approximation of the experimental data, in contrast to the PFOM which can not be applied to describe the SiO$_2$ opals adsorption kinetics, especially opals at low annealing temperatures. In Fig. 5(d), SEM parameters form quite similar regularities in the $\left ( \alpha _\mathrm {SEM}, \beta _\mathrm {SEM} \right )$ space for opals based on both the Shell- and Berry-like globules. For both opal types at lower annealing temperatures of $200$ and $400^\circ$C and for opal of Berry-like particles at $800^\circ$C, the SEM parameter is $\beta _\mathrm{SE} \neq 1$, which evidences the non-exponential transient process. In turn, for both opal types at $600 ^{\circ}$ C and for opal of Berry-like particles at $800^\circ$C, it is $\beta _\mathrm{SE} \simeq 1$, which indicates the exponential transient process, obeying the PFOM (Eq. (6)). The estimated SEM adsorption rate varies in the $\simeq 1$–$9$ hours$^{-1}$ range, and model adequately reflect changes in the adsorption rates owing to the opal annealing. It is notable that adsorption rate for both opal types at $800 ^{\circ}$ C is maximal and saturation occurs much faster than for other samples. We assume that a decrease of the adsorption saturation time for samples annealed at $800 ^{\circ}$ C is associated with a gradually porosity decreasing due to the collapse of pores caused by the sphere substructure [58]. Therefore, we conclude that SEM model can be used for the objective studies of the porous optical materials – humid atmosphere interactions.

4. Discussions

In this way, Figs. 4 and 5, revealed quite different kinetics of the water vapour adsorption by opals of the two kinds. Particularly, we observed different amount of the adsorbed water ($\sim ~N$), different rates of the adsorption process, and (what even more important) strong variability of the sample THz dielectric properties, as a function of both the annealing conditions and the hydration state. Such a variability can make the performance of such THz optical materials unstable, and, thus, can hamper their practical use in real-life applications in a humid atmosphere. In turn, from Figs. 3(d) and (h), we notice for opals of both types that their optical properties in the visible range does not change considerably during the adsorption process, and an impact of the water adsorption cannot be detected and analyzed by a naked eye. This highlights an importance of studying the effects of moisture adsorption by porous THz optical materials before their practical use. For such applications, porous THz optical materials and elements should be judiciously designed, synthesized and processed, aimed at minimizing the water uptake and the resultant fluctuations of the THz optical properties.

The moisture adsorption kinetics is well described by PFOM for opals at higher annealing temperatures, while for the lower annealing temperatures, some discrepancies between the model and experiment are evident (Fig. 5). As follows from Ref. [55], PFOM is less suitable when the initial concentration of adsorbate is not high and the adsorbent material has a large number of active sites. Both conditions are observed in our case. First, we work with the non-saturated water vapor. Second, what is even more important, we deal with a very high material porosity of opals (including a very large number of open pores [35]), when the annealing temperature is low, $< 400~^{\circ}$ C. In such case, open pores in opals forms a highly evaluated surface with its large number of active sites. Obviously, these two reasons underlie the observed discrepancy between the PFOM and experiment at lower annealing temperatures. Therefore, in this study, we decided to use the common semi-empirical SEM approach, demonstrated much better agreement with experiment, to objectively analyze and compare experimental data for all kinds of opals. At the same time, development of the adsorption kinetics models with the specific physical meanings for such complex porous materials seems to be a challenging problem in physical chemistry / chemical physics, while it is out of the scope of this paper, that is devoted to solving the particular problem of optics and optical materials.

For the samples annealed at low temperatures, we observed very close values of the adsorbed water molecules $N$, after the transient process saturation. We attribute this effect to the particular adsorbent regeneration procedure, that is used in this study and that involves vacuum storage of a sample for a couple of hours before its exposure to a humid atmosphere. In fact, this regeneration approach (as any other) leads to some residual partial occupation of the analyte free sides before the adsorption process. For example, even the well-known low-temperature heating approach is unable to provide the complete removal of chemical adsorbed water from the porous opals [58]. The initial residual content of water in an analyte can differs for distinct opals depending on their structural and chemical properties. Particularly, it seems that the opals based on the "Berry-like" particles annealed at $400~^{\circ}$ C has higher ability to adsorb water than others annealed at $200~^{\circ}$ C (Fig. 5). At the same time, we stress that the applied approach and regimes of the sample regeneration were equal for all the considered samples, that allowed us to objectively analyze and compare the kinetics of water vapor adsorption by different opals.

Despite a case study of water uptake from a humid atmosphere by nanoporous SiO$_2$-based opals [35,36] was performed in this paper, this problem should be general for all porous THz optics (depending on the amount of open pores and water-absorbing / water-resistant status), including the microstructured and 3D printed polymers [30,34], porous aerogels [31], silk foam [32] porous ceramics [33], pressed micropowderes [21], etc. However, their interactions with a humid atmosphere are still to be investigated, while the described approach involving THz pulsed spectroscopy opens the way for solving this problem. To further improve the accuracy, it can also be aided by the sample weighting, as described in Refs. [42,43]. Despite the particular parameters of a humid atmosphere considered in our work, in future studies, in would be better to resort to the certain parameter specific for some THz applications.

We can point few ways of protecting the porous THz optical materials from a humid atmosphere and sustaining their THz response unaltered during the long-term operation. First, for this, a porous material can be encapsulated by a thin polymer film, that can also serve as a dielectric support (Shell) [21] and an anti-reflection coating [41]. Second, a porous material can be infiltrated by some low-refractive-index polymer [21], but this will also somewhat improve the effective refractive index and absorption coefficient of a materials in the THz range. Third, some hydrophobic coating can be applied to the highly-evaluated surface of a porous material, but this will simultaneously improve the THz power loss. Fourth option is to use a porous material with mostly closed pores (such as opals annealed at high temperatures [35]), which adsorb much less water. However, this approach considerably limits the range of appropriate annealing temperatures and, thus, the resultant variability of THz optical properties. Detailed analysis of the listed opportunities is out of the scope of this paper.

5. Conclusions

In this paper, THz pulsed spectroscopy is used to study kinetics of water adsorption from a humid atmosphere by porous optical materials, using the nanoporous SiO$_2$-based opals as an example. From the THz data, we estimated evolution of the THz dielectric response of an analyte during adsorption, amount of the adsorbed water, and parameters of the adsorption kinetics. Our findings revealed notable changes in the THz material properties caused by a humid atmosphere, that are general for all porous optical materials and can hamper their real-life THz applications.

Funding

Russian Science Foundation (22–72–10033, 22–79–10099).

Acknowledgements

V.E.U., G.R.M. and G.M.K. acknowledge the Russian Science Foundation (RSF), Project # $22$–$72$–$10033$ (fabrication and THz spectroscopy of the opal samples). A.A.G. and K.I.Z. acknowledge the RSF Project # $22$–$79$–$10099$ (THz spectroscopy of the opal samples and analysis of the THz data and adsorption kinetics).

Disclosures

The authors declare no conflict of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time, but may be obtained from the authors upon request.

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Moisture adsorption by porous terahertz optical materials: a case study of artificial SiO₂ opals

Abstract

1. Introduction

2. Materials and methods

2.1 Sample preparation

2.2 THz pulsed spectrometer and dielectric properties reconstruction

2.3 Estimation of the adsorption parameters

3. Results

4. Discussions

5. Conclusions

Funding

Acknowledgements

Disclosures

Data availability

References

Data availability

Cited By

Figures (5)

Equations (7)

Optical Materials Express